This work presents a new class of variational family -- ergodic variational flows -- that not only enables tractable i.i.d. sampling and density evaluation, but also comes with MCMC-like convergence guarantees. Ergodic variational flows consist of a mixture of repeated applications of a measure-preserving and ergodic map to an initial reference distribution. We provide mild conditions under which the variational distribution converges weakly and in total variation to the target as the number of steps in the flow increases; this convergence holds regardless of the value of variational parameters, though different parameter values may result in faster or slower convergence. We develop a practical implementation of the flow family using Hamiltonian dynamics combined with deterministic momentum refreshment, including a tunable step size to optimize the trade-off between simulation fidelity and computational cost. Simulated and real data experiments provide an empirical verification of the convergence theory, and demonstrate that the method provides more reliable posterior approximations than several black-box normalizing flows, as well as samples of comparable quality to those obtained from state-of-the-art MCMC methods.
翻译:这项工作提出了一个新的变式家庭类别 -- -- 异式流动 -- -- 一种新型的变式家庭 -- -- 即流动量 -- -- 不仅能够进行可移植的一.d.抽样和密度评价,而且具有类似于MCMC的趋同保证。变式流动由测量保存地图和异式地图的反复应用混合到初步参考分布中。我们提供了一种温和的条件,使变式分布随着流量增加的步骤的增加而微弱和完全与目标相容;这种趋同不论变式参数的价值如何,都维持不变,尽管不同的参数值可能会导致更快或更慢的趋同。我们利用汉密尔顿的动态加上确定性动力再生,我们开发了流动家庭的实际实施过程,包括一个金枪鱼分级大小,以优化模拟忠性和计算成本之间的权衡。模拟和实际数据实验对趋同理论提供了经验性核查,并表明该方法提供了比若干黑箱正常流动更可靠的后近光度,以及具有与从现代MC方法中获得的类似质量的样品。